Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-9y &= 6 \\ -6x-6y &= 3\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = 6x+3$ Divide both sides by $-6$ to isolate $y$ $y = {-x - \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-5x-9({-x - \dfrac{1}{2}}) = 6$ $-5x + 9x + \dfrac{9}{2} = 6$ Simplify by combining terms, then solve for $x$ $4x + \dfrac{9}{2} = 6$ $4x = \dfrac{3}{2}$ $x = \dfrac{3}{8}$ Substitute $\dfrac{3}{8}$ for $x$ back into the top equation. $-5( \dfrac{3}{8})-9y = 6$ $-\dfrac{15}{8}-9y = 6$ $-9y = \dfrac{63}{8}$ $y = -\dfrac{7}{8}$ The solution is $\enspace x = \dfrac{3}{8}, \enspace y = -\dfrac{7}{8}$.